On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements

Elena Beretta; Cecilia Cavaterra; Luca Ratti

doi:10.1088/1361-6544/ab9a1b

On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements

Elena Beretta, Cecilia Cavaterra, Luca Ratti

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model we determine an asymptotic expansion of the perturbed potential due to the presence of small conductivity inhomogeneities (modelling small ischemic regions in the cardiac tissue) and use it to detect the anomalies from partial boundary measurements. This is done by determining the topological gradient of a suitable boundary misfit functional. The robustness of the algorithm is confirmed by several numerical experiments.

Original language	English (US)
Pages (from-to)	5659-5685
Number of pages	27
Journal	Nonlinearity
Volume	33
Issue number	11
DOIs	https://doi.org/10.1088/1361-6544/ab9a1b
State	Published - Nov 2020

Keywords

Cardiac electrophysiology
Inverse problems
Nonlinear boundary value problem

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/1361-6544/ab9a1b

Cite this

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title = "On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements",

abstract = "In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model we determine an asymptotic expansion of the perturbed potential due to the presence of small conductivity inhomogeneities (modelling small ischemic regions in the cardiac tissue) and use it to detect the anomalies from partial boundary measurements. This is done by determining the topological gradient of a suitable boundary misfit functional. The robustness of the algorithm is confirmed by several numerical experiments.",

keywords = "Cardiac electrophysiology, Inverse problems, Nonlinear boundary value problem",

author = "Elena Beretta and Cecilia Cavaterra and Luca Ratti",

note = "Funding Information: The authors thank the referees for their valuable comments. The authors are grateful to Roberto Gianni for his useful suggestions. The authors thank the New York University of Abu Dhabi for its kind hospitality. The authors are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilit{\`a} e le loro applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The numerical simulations presented in this work have been performed thanks to the MATLAB library redbKIT, [24]. Publisher Copyright: {\textcopyright} 2020 IOP Publishing Ltd & London Mathematical Society",

year = "2020",

month = nov,

doi = "10.1088/1361-6544/ab9a1b",

language = "English (US)",

volume = "33",

pages = "5659--5685",

journal = "Nonlinearity",

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T1 - On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements

AU - Beretta, Elena

AU - Cavaterra, Cecilia

AU - Ratti, Luca

N1 - Funding Information: The authors thank the referees for their valuable comments. The authors are grateful to Roberto Gianni for his useful suggestions. The authors thank the New York University of Abu Dhabi for its kind hospitality. The authors are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The numerical simulations presented in this work have been performed thanks to the MATLAB library redbKIT, [24]. Publisher Copyright: © 2020 IOP Publishing Ltd & London Mathematical Society

PY - 2020/11

Y1 - 2020/11

N2 - In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model we determine an asymptotic expansion of the perturbed potential due to the presence of small conductivity inhomogeneities (modelling small ischemic regions in the cardiac tissue) and use it to detect the anomalies from partial boundary measurements. This is done by determining the topological gradient of a suitable boundary misfit functional. The robustness of the algorithm is confirmed by several numerical experiments.

AB - In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model we determine an asymptotic expansion of the perturbed potential due to the presence of small conductivity inhomogeneities (modelling small ischemic regions in the cardiac tissue) and use it to detect the anomalies from partial boundary measurements. This is done by determining the topological gradient of a suitable boundary misfit functional. The robustness of the algorithm is confirmed by several numerical experiments.

KW - Cardiac electrophysiology

KW - Inverse problems

KW - Nonlinear boundary value problem

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VL - 33

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JO - Nonlinearity

JF - Nonlinearity

IS - 11

ER -

On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements

Abstract

Keywords

ASJC Scopus subject areas

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